Question

For what value of n, are the nth term of two A.Ps : 63,65,67,..... and 3,10,17.....equal?

Answer 1

$63,65,\mathrm{67.......}$

$a=63,d=2$

$n^{th}$ term $=a+\left(n+1\right)d$

$=63+\left(n+1\right)2$

$=61+2n$

(b)

$3,10,\mathrm{17....}$

$a=3,d=7$

$n^{th}$ term $=a+\left(n-1\right)d$

$=3+\left(n-1\right)7$

$=-4+7n$

Now $n^{th}$ terms of 2 ap’s as equal

So $61+2n=7n-4$

$\Rightarrow 5n=65$

$\Rightarrow n=13$

${13}^{th}$ term of A.p.s are equal